一类广义分式规划的最优性条件和对偶  

Optimality Conditions and Duality for a Class of Generalized Fractional Programming Problems

作　　者：张彩芬[1] 吴泽忠[1] 

机构地区：[1]成都信息工程学院应用数学学院,四川成都610225

出　　处：《四川师范大学学报（自然科学版）》2014年第4期506-510,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省科技厅软科学研究计划基金(2014ZR0016)资助项目

摘　　要：函数的广义凸性在数学规划的对偶理论中起着非常重要的作用.针对广义ρ-不变凸性,研究一类广义分式规划及其对偶规划问题.在文献(J.Austral Math.Soc.,1995,A58:376-386.)提出的广义分式规划最优性必要条件的基础上,给出并证明了这类规划的一个最优性充分条件,并针对这类规划提出2个对偶模型,又在适当的条件下,进一步给出并证明这2个对偶规划相应的弱对偶定理、强对偶定理和严格逆对偶定理.Generalized convexity of functions plays an important role in mathematical programming and its dual theory. In this pa- per, under a generalized convexity-p-invexity assumptions, the dual and some questions of a class of generalized fractional programming are discussed. First, on the basis of S. Chandra, et al（J. Austral Math. Soc. , 1995, A58：376 -386. ） presented essential optimality condition for this programming, we presented and proved the sufficient optimality condition for it. Two duals are put forward, and then the results about the weak duality, strong duality, and strict converse duality theorems are proved under suitable conditions.

关 键 词：ρ-伪不变凸 ρ-拟不变凸 弱对偶 强对偶 严格逆对偶 

分 类 号：O221.2[理学—运筹学与控制论]